Congressional Republicans were flummoxed Sunday by President Donald Trump's and his White House’s continued assertions — provided without evidence — that President Barack Obama had wiretapped Trump Tower during the 2016 presidential campaign.

A day after Trump made the charge, Hill Republicans were largely mute, and those who spoke out were perplexed at the source of Trump’s information, which the White House has yet to disclose.

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Sen. Marco Rubio said Sunday he had seen “no evidence” to back up Trump’s wiretap claims. Rubio is a member of the Senate Intelligence Committee, which is investigating Trump’s ties to Russia and has received classified briefings on the issue.

“I'd imagine the president and the White House in the days to come will outline further what was behind that accusation,” the Florida Republican said on NBC’s “Meet the Press.” “The president put that out there, and now the White House will have to answer as to exactly what he was referring to.”

Rubio’s comments came a day after Nebraska GOP Sen. Ben Sasse, a longtime Trump critic, said Trump owed it to the public to share more details about his allegation. Other Republican lawmakers who have clashed with Trump made similar demands for more information.

“It would be more helpful if he turned over to the intelligence committee any evidence that he has,” said Sen. Susan Collins (R-Maine), a member of the Senate Intelligence Committee, on CBS' "Face the Nation."

Trump suggested Saturday that “a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election!” In a separate tweet, he wrote “Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!”

Trump’s allegations raised questions about whether federal authorities had obtained a legal warrant to tap Trump's or his associates’ calls, perhaps through the Foreign Intelligence Surveillance Court, which can authorize wiretaps against potential foreign spies. Those orders are typically classified, and Trump’s comments sent Washington scrambling to understand his allegations.

One lawmaker who did support his call for an investigation was Rep. Devin Nunes (R-Calif.), the head of the House intelligence panel. "The Committee will make inquiries into whether the government was conducting surveillance activities on any political party’s campaign officials or surrogates, and we will continue to investigate this issue if the evidence warrants it,” he said in a statement.

But otherwise, even some of Trump's strongest supporters were cautious about rushing to his defense.

On "Fox News Sunday," Sen. Tom Cotton (R-Ark.) said he had no evidence that what Trump said was true: "It doesn't mean that none of these things have happened, just means I haven't seen them yet."

Part of the confusion stems from the fact that, according to GOP sources, the White House gave no advance notice to congressional Republicans that Trump would be raising the issue of wiretaps this weekend, leaving both sides scrambling to figure out what Trump was referring to and how to respond publicly.

Meanwhile, congressional Democrats said Trump’s flailing at his predecessor is a sign that he’s feeling squeezed by the federal investigation into his associates’ ties to Russia. Senate Minority Leader Chuck Schumer of New York said Trump’s charge, if proved false, is proof he “doesn’t know how to conduct himself.” And if it’s true, “it’s even worse,” because it means federal authorities saw a legal basis to authorize a wiretap, which requires a judge’s signoff.

“Either way … the president is in trouble,” Schumer said on “Meet the Press.”

House Democratic leader Nancy Pelosi of California said on CNN’s “State of the Union” that Trump’s allegation about Obama was a classic diversion tactic.

“This is called a wrap-up smear,” she said. “You make up something, then you have the press write about it, then you say everybody is writing about this charge. It’s the tool of an authoritarian, to just have you always be talking about what you want them to be talking about it.”

Rep. Adam Schiff, the ranking Democrat on the House intelligence panel, was also highly critical: "For a president of the United States to make such an incendiary charge — and one that discredits our democracy in the eyes of the world — is as destructive as it was baseless."

Sen. Mark Warner, the top Democrat on the Senate intelligence panel, said Sunday that he’ll be visiting with intelligence officials this week for an “unprecedented” look at the intelligence behind allegations of Russian meddling in the 2016 election and potential connections to Trump associates. The Virginia lawmaker added that he had seen no evidence — despite Trump’s claims — that federal officials had authorized a wiretap of Trump Tower, Trump’s campaign headquarters.

“We are early into this investigation,” he said, praising Republican colleagues on the committee like Rubio, Collins and Missouri Sen. Roy Blunt for cooperating with Democrats on the probe.

Warner’s comments followed a similar assertion by former Director of National Intelligence James Clapper, who said “I can deny” that there was any request by the FBI for a warrant to tap phones in Trump Tower.

"It's in everyone's interest — the current president's interest, Democrats' interest, Republicans' interest, the country's interest — to get to the bottom of all this, because it's such a distraction. Certainly the Russians have to be chortling at the success of their efforts to sow dissension in this country," he said on NBC’s “Meet the Press.”

Clapper added that he continues to believe that Russia meddled in the election on Trump's behalf, as U.S. intelligence agencies concluded in a declassified January report, but that "no evidence of collusion" between Moscow and Trump aides has been discovered.

Trump aides were caught Sunday defending the president’s accusation about Obama without any evidence to back them up. And they sought to shift the focus to Congress, by calling on the House and Senate intelligence committees — already probing potential Trump ties to Russia — to include an investigation of any illegal wiretapping by the Obama administration.

“I think what is necessary is Congress doing its job. Let them investigate,” said deputy White House press secretary Sarah Huckabee Sanders in an interview on ABC’s “This Week.”

Sanders presented no evidence of any improper actions by the Obama administration, and she refused to repeat Trump’s explosive Saturday tweets accusing Obama of spying on him and his team. Pressed repeatedly by host Martha Raddatz, Sanders said Trump was merely wondering about illegal wiretapping — despite Trump declaring it as fact just a day earlier.

“I think he is going off of information that he’s seeing that has led him to believe this is a very real potential,” she said, adding, “He’s talking about: ‘Could this have happened?’”

Trump on Saturday said that Obama had tapped Trump Tower phones, despite no evidence of his predecessor’s involvement. His claim appeared to be based on right-wing media reports raising questions about whether Trump associates had been surveilled. On Sunday, the press secretary stated: "President Donald J. Trump is requesting that as part of their investigation into Russian activity, the congressional intelligence committees exercise their oversight authority to determine whether executive branch investigative powers were abused in 2016."

Obama White House spokesman Josh Earnest insisted Sunday that any wiretaps authorized against Trump or his associates arose only from legal law enforcement authority.

“The president of the United States does not have the authority to unilaterally order the wiretapping of an American citizen,” he said, noting that such taps are approved by judges based only on evidence in a criminal or counterintelligence investigation.

Earnest said the White House kept FBI investigations at arm’s length and didn’t attempt to “influence or dictate” how those probes were conducted.

The Trump administration’s call for Congress to investigate wiretaps targeting Trump or his associates comes as the House and Senate intelligence committees have already launched probes into whether top Trump allies had contacts with Russian officials during the 2016 campaign. Nunes has also emphasized that he intends to probe leaks of classified information that have made their way into media reports since the election.

The general consensus Sunday was that the controversy indicated that more light needs to be shined on Russian meddling in the election.

"It underscores the necessity, and indeed the inevitability, of an independent investigation," Tom Donilon, Obama's national security adviser from 2010 to 2013, told Fareed Zakaria on CNN's "Fareed Zakaria GPS."